Can I use my vibration excercise plate?

I would think you are ok to use the machine at this point. Best advice is to check with your operating surgeon. They know what they have done at surgery and should be monitoring your postoperative recovery.

If it has only been one month since your surgery, it would not be advisable to vibrate the tissues that are just starting to heal.  An analogous situation is motorcycle riding, which i=I suggest the patients refrain from for 3 months after tummy tuck.

Congratulations on having undergone the tummy tuck and liposuction procedures. Ultimately, it will be important for you to “listen to your body” and resume exercise activities gradually and cautiously. Always best to check with your own plastic surgeon who knows exactly how you are progressing and what activities you wish to return to. By the way, cool machine! Best wishes for an outcome that you will be very pleased with.

In general you want to avoid core exercises for 2-3 months after a tummy tuck. As far as liposuction, you're okay to start exercise after 1 month. However, these are my standards. You should contact your surgeon to determine his protocols.